Qingxiang Xu

activity

20102026

most citedSeminorm and numerical radius inequalities of operators in semi-Hilbertian spaces

79 citations · 210 across the 18 of their papers we have counts for

collaborators

18 papers

math.FA2026

Norm attainment of a class of block operator matrices

Kangjian Wu, Jiayu Ling, Qingxiang Xu

Given complex numbers $a, b, c$ and a non-negative continuous function $φ$ defined on $[0, + \infty)$ , consider the $2 \times 2$ matrix $$ M_t = \begin{pmatrix} a & t \\ ct & bφ(t)…

math.OA2023★ 1 cited

The matched projections of idempotents on Hilbert $C^{*}$ -modules

Xiaoyi Tian, Qingxiang Xu, Chunhong Fu

The aim of this paper is to give new characterizations of some fundamental issues about idempotents. In the general setting of adjointable operators on Hilbert $C^{*}$ -modules, a new…

math.FA2022★ 3 cited

The polar decomposition of the product of three operators

Dingyi Du, Qingxiang Xu, Shuo Zhao

In the setting of adjointable operators on Hilbert $C^{*}$ -modules, this paper deals with the polar decomposition of the product of three operators. The relationship between the pola…

math.OA2022

The $(n + 1)$ -centered operator on a Hilbert $C^{*}$ -module

Na Liu, Qingxiang Xu, Xiaofeng Zhang

Let $T$ be an adjointable operator on a Hilbert $C^{*}$ -module such that $T$ has the polar decomposition $T = U T ∣$ . For each natural number $n$ , $T$ is called an $(n + 1)$ -centered opera…

math.OA2022

$C^{}$ -isomorphisms associated with two projections on a Hilbert $C^{}$ -module

Chunhong Fu, Qingxiang Xu, Guanjie Yan

Motivated by two norm equations used to characterize the Friedrichs angle, this paper studies $C^{*}$ -isomorphisms associated with two projections by introducing the matched triple a…

math.FA2020

Some upper bounds for the $A$ -numerical radius of $2 \times 2$ block matrices

Qingxiang Xu, Zhongming Ye, Ali Zamani

Let $A = (A 0 0 A)$ be the $2 \times 2$ diagonal operator matrix determined by a positive bounded operator $A$ . For semi-H…

math.FA2019★ 79 cited

Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces

M. S. Moslehian, Q. Xu, A. Zamani

Let $A$ be a positive bounded operator on a Hilbert space $(H, ⟨ \cdot, \cdot ⟩)$ . The semi-inner product ${\langle x, y\rangle}_A := \langle Ax, y\ra…

math.FA2019★ 5 cited

Numerical radius inequalities concerning with algebraic norms

A. Zamani, M. S. Moslehian, Q. Xu +1

We give an expression for a generalized numerical radius of Hilbert space operators and then apply it to obtain upper and lower bounds for the generalized numerical radius. We also…

math.FA2019★ 18 cited

Halmos' two projections theorem for Hilbert $C^{*}$ -module operators and the Friedrichs

Wei Luo, Mohammad Sal Moslehian, Qingxiang Xu

Halmos' two projections theorem for Hilbert space operators is one of the fundamental results in operator theory. In this paper, we introduce the term of two harmonious projections…

math.FA2019★ 48 cited

Positivity of $2 \times 2$ block matrices of operators

Mohammad Sal Moslehian, Mohsen Kian, Qingxiang Xu

We review some of the significant generalizations and applications of the celebrated Douglas theorem on the equivalence of factorization, range inclusion, and majorization of opera…

math.OA2018★ 2 cited

The polar decomposition for adjointable operators on Hilbert $C^{*}$ -modules and centered operators

Na Liu, Wei Luo, Qingxiang Xu

Let $T$ be an adjointable operator between two Hilbert $C^{*}$ -modules and $T^{*}$ be the adjoint operator of $T$ . The polar decomposition of $T$ is characterized as $T=U(T^*T)^\frac12…

math.OA2018

The polar decomposition for adjointable operators on Hilbert $C^{*}$ -modules and $n$ -centered operators

Na Liu, Wei Luo, Qingxiang Xu

Let $n$ be any natural number. The $n$ -centered operator is introduced for adjointable operators on Hilbert $C^{*}$ -modules. Based on the characterizations of the polar decomposition…

math.OA2018★ 5 cited

The parallel sum for adjointable operators on Hilbert $C^{*}$ -modules

Wei Luo, Chuanning Song, Qingxiang Xu

The parallel sum for adjoinable operators on Hilbert $C^{*}$ -modules is introduced and studied. Some results known for matrices and bounded linear operators on Hilbert spaces are gen…

math.FA2018

New multiplicative perturbation bounds for the generalized polar decomposition

Na Liu, Wei Luo, Qingxiang Xu

Some new Frobenius norm bounds of the unique solution to certain structured Sylvester equation are derived. Based on the derived norm upper bounds, new multiplicative perturbation…

math.OA2018★ 24 cited

Douglas factorization theorem revisited

Vladimir Manuilov, Mohammad Sal Moslehian, Qingxiang Xu

Inspired by the Douglas lemma, we investigate the solvability of the operator equation $A X = C$ in the framework of Hilbert C*-modules. Utilizing partial isometries, we present its g…

math.FA2018★ 11 cited

Perturbation estimation for the parallel sum of Hermitian positive semi-definite matrices

Wei Luo, Chuanning Song, Qingxiang Xu

Let $C^{n \times n}$ be the set of all $n \times n$ complex matrices. For any Hermitian positive semi-definite matrices $A$ and $B$ in $C^{n \times n}$ , their new c…

math.OA2017★ 14 cited

On majorization and range inclusion of operators on Hilbert $C^{*}$ -modules

Xiaochun Fang, Mohammad Sal Moslehian, Qingxiang Xu

It is proved that for adjointable operators $A$ and $B$ between Hilbert $C^{*}$ -modules, certain majorization conditions are always equivalent without any assumptions on $\overline{\…

math.OA2010

Representations for weighted Moore-Penrose inverses of partitioned adjointable operators

Qingxiang Xu, Yonghao Chen, Chuanning Song

For two positive definite adjointable operators $M$ and $N$ , and an adjointable operator $A$ acting on a Hilbert $C^{*}$ -module, some properties of the weighted Moore-Penrose inverse…

Norm attainment of a class of block operator matrices

The matched projections of idempotents on Hilbert C∗-modules

The polar decomposition of the product of three operators

The (n+1)-centered operator on a Hilbert C∗-module

C∗-isomorphisms associated with two projections on a Hilbert C∗-module

Some upper bounds for the A-numerical radius of 2×2 block matrices

Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces

Numerical radius inequalities concerning with algebraic norms

Halmos' two projections theorem for Hilbert C∗-module operators and the Friedrichs

Positivity of 2×2 block matrices of operators

The polar decomposition for adjointable operators on Hilbert C∗-modules and centered operators

The polar decomposition for adjointable operators on Hilbert C∗-modules and n-centered operators

The parallel sum for adjointable operators on Hilbert C∗-modules

New multiplicative perturbation bounds for the generalized polar decomposition

Douglas factorization theorem revisited

Perturbation estimation for the parallel sum of Hermitian positive semi-definite matrices

On majorization and range inclusion of operators on Hilbert C∗-modules

Representations for weighted Moore-Penrose inverses of partitioned adjointable operators

The matched projections of idempotents on Hilbert $C^{*}$ -modules

The $(n + 1)$ -centered operator on a Hilbert $C^{*}$ -module

$C^{}$ -isomorphisms associated with two projections on a Hilbert $C^{}$ -module

Some upper bounds for the $A$ -numerical radius of $2 \times 2$ block matrices

Halmos' two projections theorem for Hilbert $C^{*}$ -module operators and the Friedrichs

Positivity of $2 \times 2$ block matrices of operators

The polar decomposition for adjointable operators on Hilbert $C^{*}$ -modules and centered operators

The polar decomposition for adjointable operators on Hilbert $C^{*}$ -modules and $n$ -centered operators

The parallel sum for adjointable operators on Hilbert $C^{*}$ -modules

On majorization and range inclusion of operators on Hilbert $C^{*}$ -modules